Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-10-31T14:13:42Z No. of bitstreams: 1 marciosafortes.pdf: 648269 bytes, checksum: 283586f68cccd517cd4b33663a174533 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-12-15T13:13:35Z (GMT) No. of bitstreams: 1 marciosafortes.pdf: 648269 bytes, checksum: 283586f68cccd517cd4b33663a174533 (MD5) / Made available in DSpace on 2016-12-15T13:13:35Z (GMT). No. of bitstreams: 1 marciosafortes.pdf: 648269 bytes, checksum: 283586f68cccd517cd4b33663a174533 (MD5) Previous issue date: 2007-09-28 / Este trabalho tem por objetivo analisar como a mineiridade como ideologia é utilizada, no caso concreto do PSDB, para criar coesão na classe dominante; legitimar sua dominação; e principalmente, posicionar a fração mineira em relação ao partido, o sistema partidárioeleitoral e o restante do país. Este tema se relaciona ao modo como as disputas das frações partidárias pelo controle das zonas de incerteza, da distribuição dos incentivos coletivos e seletivos e pela ocupação do posto de coalizão dominante. No primeiro capítulo trataremos do tema da ideologia e da mineiridade procurando conceitua-los para resolução de nossas questões. O segundo capítulo abrangerá a temática da tória partidária e da teoria das organizações a fim de nos fornecer ferramentas para a análise das disputas entre as frações partidárias e da ação do PSDB-MG. Por fim, no terceiro capitulo, procuramos articular os conceitos definidos nos dois primeiros capítulos aplicando-os na trajetória do PSDB nacional e mineiro. / This work aims to analyze how the “mineiridade” as an ideology is applied, in the concrete case of the Party of Brazilian Social Democracy (Partido da Social Democracia Brasileira - PSDB), so as to create cohesion among the dominant class; legitimize its dominance; and mainly, situate the “mineira” wing in the party, in the party electoral system and in the rest of the country. This theme is related to the struggle among the party fractions for control over the uncertainty zones, the distribution of collective and selective incentives, and the position as dominant coalition. The first chapter discusses ideology and “mineiridade”, seeking to conceptualize them to answer our questions. The second chapter embraces the party theory and organization theory in order to provide us with the tools for the analysis of struggles among the party fractions and the action of the PSDB-MG. Finally, the third chapter seeks to articulate the concepts defined in the first two chapters applying them to the trajectory of national PSDB and its “mineira” wing.

FundaÃÃo de Amparo à Pesquisa do Estado do Cearà / The primary concern of the present research is fractionsâ content, focusing on the relevance of such mathematical content to logical-mathematical acquisition. Firstly, a discussion on pedagogueâs early instruction is done, since this professionalâs grounding enables her to teach Mathematics in early series and so it needs to be improved. The aim of this study is to observe how Fedathiâs Sequence methodology, connected with Didactic Engineering, can contribute to enhance the teaching and learning practices of fractions, theoretically and methodologically supported by pedagogical workshops and by the TelEduc Platform. Therefore, the main question this work answers is whether Fedathiâs Sequence methodology, connected with Didactic Engineering, contributes to decrease lacks in the apprehension of the concept of fraction. Participative research methodology scaffolded this work, since it was considered necessary to comprehend the action and participation of investigated subjects. These were students of the 7th semester of the Pedagogy course from the Faculty of Education belonging to Universidade Federal do Ceara. The analysis pointed to the following results: a) the students-teachers have a limited background on fractions; b) they do not know available methodologies to teach Maths; c) there is little contact with information technologies. Thus, the researchers worked to operate real changes in their relationship with fractionsâ content, favoring the attainment of new schemes and restructuring other consolidated ones. It was possible to provide a discussion on the knowledge they already had and the knowledge they thought they had, observing these concerns within the re-elaboration of a new discourse of theirs. It was concluded, during the whole groundwork, that the investigated subjects, that is, future teachers made explicit the need for more study on the subject, in order to develop autonomy and a full reflection on the relation between docentâs theory and practice. / O ponto de fulcro desta pesquisa à o conteÃdo das fraÃÃes, destacando-se a relevÃncia deste conteÃdo matemÃtico para a aquisiÃÃo do conhecimento lÃgico-matemÃtico. Inicia-se este trabalho, fazendo uma discussÃo sobre a formaÃÃo inicial do pedagogo, tendo em vista que o preparo deste profissional lhe permitirà ir para as salas de aula lecionar MatemÃtica para as sÃries iniciais e precisa ser bem trabalhado. Objetiva-se com esta pesquisa observar de que modo as metodologias SeqÃÃncia Fedathi, aliadas à Engenharia DidÃtica, podem contribuir para a melhoria do ensino e da aprendizagem de fraÃÃes, tendo como suporte teÃrico e metodolÃgico o uso de oficinas pedagÃgicas e da plataforma TelEduc. Neste sentido, responde-se com esta pesquisa a questÃo principal, mÃvel da realizaÃÃo deste estudo, que foi âverificar se as metodologias de ensino Engenharia DidÃtica e SeqÃÃncia Fedathi contribuem para minimizar as dificuldades na apreensÃo do conceito de fraÃÃoâ. A metodologia de suporte foi a pesquisa-participante, por se considerar a necessidade de aÃÃo e participaÃÃo dos sujeitos investigados. Os sujeitos investigados foram alunos do sÃtimos semestre do curso de Pedagogia da Faculdade de EducaÃÃo da Universidade Federal do CearÃ-FACED/UFC. As anÃlises apontaram os seguintes resultados: a) os alunos-professores tÃm uma visÃo estreita sobre as fraÃÃes; b) desconhecem as metodologias para o ensino de MatemÃtica; c) tÃm concepÃÃes sobre o assunto que nÃo sÃo as reais; d) hà pouco contato com as tecnologias de informaÃÃo. Desta forma, trabalhou-se para operar mudanÃas reais em suas relaÃÃes com o conteÃdo das fraÃÃes, promovendo a consecuÃÃo de novos esquemas e reestruturando outros jà consolidados. Foi possÃvel promover uma discussÃo sobre o que eles jà sabiam sobre o conteÃdo e o que pensavam que sabiam, sendo observadas essas preocupaÃÃes na reelaboraÃÃo de um novo discurso por parte deles. Concluiu-se que, durante a formaÃÃo, que os sujeitos investigados, ou seja, os futuros-professores, explicitaram a necessidade de estudar mais o assunto abordado, para desenvolver autonomia e ampla reflexÃo acerca da relaÃÃo da teoria com a prÃtica docente.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Objetivou-se com o presente estudo caracterizar as fraÃÃes de carboidratos e proteÃna e estimar o valor energÃtico e a digestibilidade intestinal da proteÃna nÃo-degradada no rÃmen de alimentos por intermÃdio da tÃcnica de trÃs estÃgios da algaroba (Prosopis juliflora), da canafÃstula (Pithecellobium multiflorum), da flor-de-seda (Calotropis procera), da jitirana (Ipomea sp.), do juazeiro (Zizyphus joazeiro), do mata-pasto (Senna obtusifolia), do sabià (Mimosa caesalpiniaefolia), da palma gigante (Opuntia fÃcus indica) e do xique-xique (Cereus gounellei) e dos subprodutos do abacaxi (Ananas comosus), da acerola (Malpighia emarginata), do caju (Anacardium occidentale), do coco (Cocos nucifera), do melÃo (Cucumis melo), do maracujà (Passiflora eduli), da uva (Vitis labrusca) e do urucum (Bixa orellana). Para obtenÃÃo do fracionamento dos carboidratos, de acordo com o sistema CNCPS, foram calculados os carboidratos totais, as suas fraÃÃes B2, C e os componentes solÃveis em detergente neutro. Foram determinadas as fraÃÃes potencialmente degradÃvel (B2) e nÃo-degradÃvel (C) da fibra em detergente neutro, corrigida para cinzas e proteÃna. Para determinaÃÃo das fraÃÃes nitrogenadas, foram analisados os compostos nitrogenados nÃo-protÃicos, nitrogÃnio solÃvel e insolÃvel em tampÃo borato-fosfato e nitrogÃnio protÃico insolÃvel em detergente neutro e em detergente Ãcido. Para a estimaÃÃo dos Nutrientes DigestÃveis Totais (NDT) foram utilizadas as equaÃÃes propostas pelo NRC (2001). Para a determinaÃÃo da digestibilidade intestinal da proteÃna nÃo-degradada no rÃmen, os alimentos foram inicialmente incubados no rÃmen de fÃmea bovina fistulada, por 16 horas para determinaÃÃo da ProteÃna nÃo-degradada no rÃmen (PNDR), sendo o resÃduo submetido à digestÃo com soluÃÃo de pepsina durante 1 hora, e soluÃÃo de pancreatina a 38ÂC durante 24 horas, cujos resÃduos foram analisados para nitrogÃnio total. Acerola e melÃo apresentaram substancial conteÃdo nitrogenado na fraÃÃo C o que reduziria a disponibilidade de N tanto para microrganismos do rÃmen quanto para o hospedeiro. As forrageiras estudadas apresentaram maiores proporÃÃes do nitrogÃnio nas fraÃÃes A e B2, consequentemente disponibilizando nitrogÃnio para bactÃrias fermentadoras de carboidratos fibrosos. O percentual de fraÃÃo C na acerola e no melÃo em detrimento da fraÃÃo B2 acarretaria maior efeito de repleÃÃo ruminal e diminuiÃÃo da disponibilidade energÃtica, por sua caracterÃstica de indigestibilidade ao longo do trato gastrointestinal, quando submetidos a ensaios de alimentaÃÃo para animais. Nas forrageiras nativas e nas adaptadas ao clima da regiÃo Nordeste foram observados valores de fraÃÃo A + B1 de 35,26 a 73,37%, para fraÃÃo B2, de 3,87% a 28,45% e para fraÃÃo C de 17,34 e 40,63%. As fraÃÃes A, B1, B2, B3 e C dos compostos nitrogenados apresentaram variaÃÃo de 9,84 a 42,33 %; 1,58 a 11,47%; 48,63 a 80,10%; 0,70 a 6,13% e 0,43 a 2,86%, respectivamente. As fraÃÃes de carboidratos dos subprodutos analisados variaram de 19,35 a 58,52%; 9,95 a 61,44% e 15,35 a 70,06 para A+B1, B2 e C, respectivamente; enquanto para os compostos nitrogenados variaram de 5,01 a 33,02%; 1,69 a 15,23%; 2,26 a 75,60%; 1,53 a 40,26% e 0,08 a 43,84% para fraÃÃes A, B1 B2, B3 e C, respectivamente. O NDT estimado das forrageiras variou de 48,30 a 65,42%, enquanto o dos subprodutos variou de 31,41 a 128,90%. A estimativa da PNDR das forragens variou de 13,37 a 83,6%, e dos subprodutos variou de 39,14 a 89,06%. A digestibilidade intestinal da PNDR das forragens variou de 26,09 a 80,68%, enquanto para os subprodutos variou de 22,26 a 76,82%. O sabià foi a forrageira que apresentou a maior DI e o maior teor de PNDRd, e a flor-de-seda os menores valores; enquanto para os subprodutos, o melÃo apresentou o maior valor para DI, entretanto o caju forneceu maior teor de PNDRd, enquanto o coco apresentou os mais baixos valores para DI e PNDRd / The objective of this research was to characterize the protein and carbohydrate fractions,estimate energy values and evaluate the intestinal digestibility protein of algaroba (Prosopis juliflora), canafÃstula (Pithecellobium multiflorum), flor-de-seda (Calotropis procera), jitirana (Ipomea sp.), juazeiro (Ziziphus joazeiro), mata-pasto (Senna obtusifolia) and sabià (Mimosa caesalpiniaefolia Benth), palma gigante (Opuntia ficus indica) and xique-xique (Cereus gounellei) and the agroindustry byproducts from pineapple (Ananas comosus L.), barbados cherry (Malpighia emarginata), cashew (Anacardium occidentale), coconut (Cocos nucifera L.), melon (Cucumis melo), passion fruit (Passiflora eduli), grape (Vitis labrusca) and anatto seeds (Bixa orellana L.). To obtain the carbohydrates fractions, according with Cornell Net Carbohydrate and Protein System (CNCPS) system, were calculated the total carbohydrates, their fractions B2, C and the soluble components in neutral detergent. It was determinated the potentially degradable (B2) and undegradable (C)fractions of the neutral detergent fiber, corrected for ashes and protein. The non-protein nitrogenous compounds, soluble and insoluble nitrogen in borate-phosphate buffer, nitrogenous protein insoluble in neutral and acid detergent were analyzed for the determination of the nitrogen fractions. To estimate Total Digestible Nutrients (TDN) had been used the equations proposals by National Research Council - NRC (2001). The feeds were incubated in rumen during 16 hours to determine the rumen-undegradable protein (RUDP), then the residue was incubated with pepsin solution during 1 hour, and pancreatic solution during 24 hours at 38ÂC, whose residues were analyzed for total nitrogen. The Malpighia emarginata and Cucumis melo showed substantial nitrogen content in fraction C which would reduce the disponibility of nitrogen for the rumen microorganisms and its host. The evaluated forages showed higher proportions of nitrogen in fractions A and B2, providing nitrogen for the rumen microorganisms. The percentage of fraction C in Malpighia emarginata and Cucumis melo at the expense of the B2 fraction would entail greater effect of ruminal fill and decreased availability of energy, for its characteristic of indigestibility along the gastrointestinal tract, when being tested for feeding animals. In the evaluated forages had been observed values of A+B1 fraction from 35.26 to 73.37%, for B2 fraction, from 3.87% to 28.45% and for C fraction from 17.34 to 40.63%. The fractions, A, B1, B2, B3 and C of nitrogenous compounds had presented variation from 9.84 to 42.33%; 1.58 to 11.47%; 48.63 to 80.10%; 0.70 to 6.13% and 0.43 to 2.86%, respectively. The byproducts carbohydrate fractions analyzed varied from 19.35 to 58.52%; 9.95 to 61.44% and 15.35 to 70.06, for A+B1, B2 and C, respectively. In turn, the nitrogenous compounds varied from 5.01 to 33.02%; from 1.69 to 15.23%; from 2.26 to 75.60%; from 1.53 to 40.26% and from 0.08 to 43.84% for fractions, A, B1 B2, B3 and C, respectively. The forages TDN values varied from 48.30 to 65.42%, while of by-products it varied from 31.41 to 128.9%. The estimate of RUDP in the forages ranged from 13.37% to 83.6%, and the byproducts RUDP ranged from 39,14 to 89.06%. The intestinal digestion of RUDP ranged from 26.09 to 80.68%, %, while for byproducts varied of 22,26 76.82%. The Mimosa caesalpiniaefolia Benth was the forage that presented better ID and better RUDPd, and the Calotropis procera, presented lowest values for these variables. For byproducts, the Cucumis melo presented the biggest value for DI, while the Cocos nucifera L. presented the lowest values for DI and RUDPd

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / O experimento foi conduzido no campo avanÃado do NÃcleo de Pesquisa em Forragicultura - NPF (www.npf.ufc.br) localizado na Fazenda Experimental do Vale do Curu â FEVC, pertencente à Universidade Federal do Cearà â UFC. Objetivou-se avaliar a composiÃÃo quÃmica e o fracionamento dos carboidratos da biomassa de Panicum maximum cv. TanzÃnia sob trÃs perÃodos de descanso (PDs) baseados no nÃmero de novas folhas expandidas por perfilho (1,5; 2,5 e 3,5F). Utilizou-se o delineamento inteiramente casualizado em arranjo fatorial 3x3 (3 fraÃÃes e 3 PDs). A colheita das amostras foi feita antes da entrada e apÃs a saÃda dos animais dos piquetes. Posteriormente, as amostras foram separadas nas fraÃÃes folha, colmo e material morto. No LaboratÃrio de NutriÃÃo Animal do Departamento de Zootecnia da UFC (LNA/DZ/UFC), foram determinados os teores de Fibra em Detergente Neutro (FDN), Fibra em Detergente Ãcido (FDA), Hemicelulose (HEM), Celulose (CEL), Lignina (LIG), Extrato EtÃreo (EE), ProteÃna Bruta (PB), NitrogÃnio InsolÃvel em Detergente Neutro (NIDN), NitrogÃnio InsolÃvel em Detergente Ãcido (NIDA), Carboidratos Totais (CT), Carboidratos NÃo Fibrosos (CNF), e das fraÃÃes que compÃem os CT: A+B1, B2 e C. Os teores de FDN e de FDA foram elevados (P<0,05) com o avanÃo dos PDs. A planta inteira (PI) do pasto sob maior PD (3,5F), no prÃ-pastejo, apresentou teores, respectivamente, de 74,0 e 46,3% sendo estes elevados para 77,3 e 50,9% no pÃs pastejo. Os teores de LIG da fraÃÃo folha do pasto sob PD 3,5F (4,2%) sofreram elevaÃÃes (P<0,05) no prÃ-pastejo. Os teores de LIG na PI foram superiores (P<0,05) naquelas submetidas ao PD 3,5F em comparaÃÃo Ãs PIs do PD 1,5F tanto no prÃ-pastejo (4,7 e 5,3%) quanto no pÃs-pastejo (4,7 e 5,3%). Os maiores teores de PB da fraÃÃo folha foram encontrados nos pastos sob PD 1,5F (10,9 e 8,6%), no prà e pÃs-pastejo. Os teores de PB na planta inteira variaram de 8,8 a 6,4% (P<0,05) e 6,2 e 4,4% (P<0,05) entre os PDs 1,5 e 3,5F, respectivamente no prà e pÃs-pastejo. Os teores de NIDA, tambÃm foram elevados (P<0,05) na PI do PD 3,5F (20,3 e 28,5%), respectivamente no prà e pÃs-pastejo. Os teores de CT da fraÃÃo folha e da PI apresentaram teores mÃdios (P>0,05) de 75,4 e 77,4% no prÃ-pastejo e 79,2 e 89,2% no pÃs pastejo. A fraÃÃo C dos carboidratos apresentou variaÃÃo mÃdia de 11,4 a 11,9%, na fraÃÃo folha, enquanto que na PI do pasto sob PD 3,5 F, foram observados os maiores teores (P<0,05) desta fraÃÃo (14,4 e 15,7%), em ambos os casos quando observados no prà e pÃs-pastejo. O pasto de capim TanzÃnia manejado sob PD 1,5F apresentou a melhor composiÃÃo quÃmica dos que foram avaliados. Contudo à necessÃrio que informaÃÃes sobre a composiÃÃo quÃmica dos pastos sejam levadas em consideraÃÃo em conjunto com as mudanÃas ocorridas na estrutura do pasto para que se possa ter uma maior exatidÃo na avaliaÃÃo da qualidade dos pastos. / The experiment was carried out in the advanced field of the Forage Research Sector - NPF (www.npf.ufc.br) located in the Experimental Farm of the Vale do Curu - FEVC, belonging to Federal University of Cearà - UFC. The objective was evaluate the chemical composition and the carbohydrate fractionation of Panicum maximum cv. TanzÃnia biomass under three rest periods (RPs) based in the new leaf (L) number expanded for tiller (1.5; 2.5 and 3.5L). Was used the completely randomized design in a factorial arrangement 3x3 (3 fractions and 3 RPs). The harvest of the samples was made before the entrance and after the exit the animals the poles. Later, the samples had been separate in the fractions leaf, culm and death material, being droughts in greenhouse of forced ventilation 65 C for 72 hours, and processed. In the Laboratory of Animal Nutrition of the Animal Science Department of UFC (LNA/DZ/UFC), were determined the levels of Neutral Detergent Fiber (NDF), Acid Detergent Fiber (ADF), Hemi-cellulose (HC), Cellulose (CEL), Lignin (LIG), Etereal Extract (EE), Crude Protein (PB), Insoluble Nitrogen in Neutral Detergent (INND), Insoluble Nitrogen in Acid Detergent (INAD), Total Total Carbohydrates (TC), Non Fiber Carbohydrates (NFC), and of the fractions that compose the TC: A+B1, B2 and C. The levels of NDF and ADF had been raised (P<0.05) with the advance of the RPs. The entire plant (EP) of the grass under bigger RP (3.5L), in the before grazing, presented levels, respectively, of 74.0 and 46.3% being these raising for 77,3 and 50,9% after grazing. The levels of LIG of leaf fraction of the grass under RP 3.5L (4.2%) had suffered rises (P<0.05) after grazing. The LIG levels in the RP were higher (P<0.05) in those submitted to 3.5L RP in comparison to the EPs of the 1.5L RP in such a way in before grazing (4.7 and 5.3%) how much after grazing (4.7 and 5.3%). The biggest levels of PB of the leaf fraction had been found in the grass under 1.5L RP (10,86 and 8.59%), before grazing and after grazing. The levels of CP in the entire plant had varied of 8.8 6.4% (P<0.05) and 6.16 and 4.4% (P<0.05) between 3.5 and 1.5L RPs, respectively before and after grazing. The INAD levels, had been also raised (P<0.05) in the EP of 3.5L RP (20.3 and 28.5%), respectively before and after grazing. The levels of TC of the leaf fraction and the EP had presented average levels (P>0.05) of 75.4 and 77.4% before grazing and 79.2 and 89.2% after grazing. The C carbohydrates fraction presented average between 11.4 11.9%, in the leaf fraction, whereas in the EP of the grass under 3.5L RP, had been observed biggest levels (P<0.05) of this fraction (14.3 and 15.7), in both cases when observed before grazing and pos-grazing. The TanzÃnia grass under 1.5L RP presented the best chemical composition of that they had been evaluated. However, it is necessary that information on the chemical composition of the grass are taken in consideration in set with the occured changes in the structure of the grass so that if can have a bigger exactness in the evaluation of the quality of the grass.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-05-10T14:11:31Z No. of bitstreams: 1 paolalucianacorreia.pdf: 8115406 bytes, checksum: 02d3268fce947c52d18a9287fb5bf694 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-06-15T14:19:54Z (GMT) No. of bitstreams: 1 paolalucianacorreia.pdf: 8115406 bytes, checksum: 02d3268fce947c52d18a9287fb5bf694 (MD5) / Made available in DSpace on 2016-06-15T14:19:54Z (GMT). No. of bitstreams: 1 paolalucianacorreia.pdf: 8115406 bytes, checksum: 02d3268fce947c52d18a9287fb5bf694 (MD5) Previous issue date: 2015-07-31 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Esta proposta de ensino foi aplicada em uma turma de 9o ano de uma escola pública de Visconde do Rio Branco. Constatamos que neste nível escolar, ao contrário do que se é esperado pelos Parâmetros Curriculares Nacionais (PCNs), os alunos ainda não têm domínio em reconhecer nem operar com os números racionais. Por essa razão, buscamos ao longo do nosso trabalho reconstruir os conceitos de fração, bem como consolidar os algoritmos utilizados para desenvolver as operações básicas com tais números, visando assim fixar a aprendizagem desses conteúdos. Para atingir tais objetivos, fizemos o uso do software Geogebra, que é um software gratuito, e realizamos atividades com dobraduras para reforçar o aprendizado. Concluímos que tal trabalho contribuiu consideravelmente para o ensino e aprendizagem de tais alunos e que outros professores podem levar tais ferramentas para auxiliar suas aulas. / The following proposal for teaching was aplied in a class of ninth grade in a public school of Visconde do Rio Branco. We noted that, in this school, unlike the level proposed by the National Curricular Parameters (PCNs), the students still have no domain to recognize or operate with the rational numbers. For this reason, the aim of our work was to re-build the concept of fraction as well as consolidate the algorithms used to develop the basic operations with such numbers. To achieve these goals, we made use of the software Geogebra, which is free software, and we performed activities with foldings to reinforce learning. We concluded that this work contributed significantly to the teaching and learning of such students and other teachers can take these tools to assist their classes.

[pt] A idéia central desta tese foi trabalhar o conceito de fração, identificando a fração como número e representando esse número na reta numérica, tendo como base as recomendações e experiências realizadas por Kathleen Hart, e principalmente Hung-Hsi Wu. Um conjunto de atividades foi desenvolvido, constituindo uma proposta de ensino de frações, posta em prática em turmas do sétimo ano e oitavo ano do Colégio Pedro II durante os anos letivos de 2006 e 2007. Parte substancial da tese é dedicada à descrição dos procedimentos metodológicos desenvolvidos para a aplicação dos princípios teóricos defendidos e de aspectos da implementação desses procedimentos em sala de aula. Grande número de exemplos das atividades realizadas é apresentado, dando-se destaque às resposta dos alunos às mesmas. O acompanhamento da evolução dos alunos é amplamente documentado. Os resultados são avaliados tanto do ponto do vista global quanto do ponto de vista de grupos diferenciados de alunos em diferentes níveis de qualificação prévia. O encaminhar de todo o trabalho investigativo leva a duas conclusões essenciais: a familiarização com o campo algébrico é alcançada com mais facilidade quando o conceito de fração é trabalhado na forma proposta; o envolvimento com as atividades e a compreensão pelos alunos da construção que estavam realizando em relação aos conceitos propostos devolvem o interesse das crianças pela aprendizagem da Matemática, fundamental para o êxito de qualquer proposta pedagógica. / [en] The main idea of this thesis was to work on the concept of fraction, identifying the fraction as a number and representing it in the line, taking as basis the recommendations and experiments of Kathleen Hart, and, mainly Hung-Hsi Wu. A set of activities was developed, generating a proposal for teaching fractions, led to practice in classes of students of 7th and 8th grade of Colegio Pedro II during the school years of 2006 and 2007. A substantial part of the thesis is devoted to the description of the methodological procedures developed for the implementation of the theoretical principles defended and of aspects of the implementation of these procedures in the classroom. Large number of examples is given of the activities performed, emphasis being given to the response of the students. The monitoring of the progress of the students is widely documented. The results are evaluated from the global point of view and considering distinct groups of students at different levels of prior qualification. The development of all the research work led essentially to two conclusions: the familiarization with the algebraic field is more easily reached when the concept of fraction is dealt in the proposed way; the involvement of the students with the activities and their understanding of the construction that they were doing with the concepts proposed returned them the interest for learning mathematics, the key to the success of any educational proposal.

Syftet med denna rapport är att utveckla ett analytiskt tänkande vid val av läromedel i sin undervisning. Med fokus på det matematiska innehållet bråk och dess kritiska aspekter och förekommande variationsmönster i bråkuppgifter analyseras två läromedel för årskurs 6.   Metoden som valdes var en mindre kvalitativ läromedelsanalys. Två läromedel för årskurs 6 analyserades med syfte att undersöka vilka variationsmönster som förekommer i uppgifter om bråk och hur de kritiska aspekterna gestaltades. De kritiska aspekter som valdes var begreppet bråk, helheten av bråk samt förenkla och storleksordna bråk.   Efter att ha analyserat läromedlen kunde det konstateras att förekomsten av olika variationsmönster är god, men att variationen av mönster är olika i de båda läromedlen. De kritiska aspekter som förbestämdes förekom i samtliga analyserade läromedel och gestaltades på olika sätt. Det ena läromedlet hade ett mer framstående kapitel om bråk med tydlighet för att överbrygga svårigheter. Det andra läromedlet hade ett mer gediget arbete med tallinjen, vilken var helt utesluten i det förstnämnda läromedlet.   Efter vår studie dras slutsatsen att de läromedel som analyserats mycket väl kan vara fullgoda att använda som enda källa i sin undervisning Men att de inte sällan bör kompletteras med annat material och andra källor för att göra undervisningen komplett och uppfylla de förmågor som ligger till grund för kunskapskraven i gällande läroplan.

The diploma thesis is aimed at reeducation of mechanical knowledge in the area of fractions. Since every student has different needs and pace in his/her process of gaining knowledge, the reeducation is set into their private supplementary tutoring lessons. In the theoretical part, the basic concepts (how is the private supplementary tutoring understood in this thesis, which students are taken into consideration, and what is mechanical knowledge) are explained based on Czech and foreign literary sources, subsequently, the constructivist way of teaching, which is suitable for the reeducation of mechanical knowledge, is described. The second part of this thesis is constituted by the practical implementation of the theoretical findings into three case studies. Three students were diagnosed with mechanical knowledge in the area of fractions. Subsequently, their knowledge was being reeducated during their private supplementary tutoring lessons. The process of reeducation of each student is described in detail, moreover, a kind of manual describing what should not be avoided when dealing with this topic is included. KEY WORDS mechanical knowledge, reeducation, private supplementary tutoring, fractions 5

In the classroom, teachers make use of different combinations of social planes (e.g., individual, collaborative) to support learning. However, little is known about the complementary strengths of individual and collaborative learning or how to combine them so that they are more effective than either social plane alone. One roadblock to this investigation is an ability to orchestrate, or manage, more complex, but theoretically effective, combinations of collaborative and individual learning in the classroom. Prior research has created orchestration tools that support the planning and real-time management of classroom activities, which reduces the cognitive load and time needed for instructors to support the activity, allowing for more complex activities to become more manageable. Current orchestration tools do not, however, support a wide range of combinations of collaborative and individual learning activities in a flexible manner. To fully investigate the combinations of collaborative and individual learning, orchestration tools need to be developed that can support the researcher in a way that can be integrated into the classroom by accounting for teachers’ values. My thesis work addresses two related goals. First, my work addresses the questions: Do collaborative and individual learning have complementary strengths and is a combination of the two social planes better than either alone? In my work, I developed an intelligent tutoring system (ITS) to support collaborative and individual learning. Through three studies, using this ITS, with over 500 4th and 5th grade students, I demonstrate that a collaborative ITS can be used to effectively support learning with elementary school students and that a combination of collaborative and individual learning is more effective than either alone. However, my studies did not find any support for complementary strengths and many other combinations of social planes are left to investigate. Additionally, during my experiments, I encountered challenges in orchestration that, along with the need to research more complex combinations of collaborative and individual learning, informed the next steps of my research. The second question my thesis work addresses is: How does an orchestration tool that supports researchers in exploring this space need to be designed to align with teachers’ values for easy integration in the classroom? Specifically, I aimed to support fluid transitions between social planes where students do not all have to be working in sync, which is not currently supported in existing orchestration tools. To support the orchestration tool design, I present a framework that structures the space that a researcher can explore when combining individual and collaborative learning. The framework can act as the set of requirements to be met in the orchestration tool from the point of the researcher as well as a lens to analyze and design combined social plane activities. As a first step towards supporting fluid transitions as laid out in the framework, I present a set of statistical models that extend domain-level individual modeling into the space of collaborative environments. Finally, I developed an orchestration prototype built around my framework that can be used as a research tool to further explore combined collaborative and individual spaces. To develop the tool to be successful within the classroom, I worked with teachers through a co-design process and validation of the prototype to incorporate their values into the tool. Taken together, my dissertation has six primary contributions. My dissertation contributes to the learning sciences through advancing our knowledge of (1) the strengths of collaborative and individual learning, although I did not find any complementary strengths, and (2) if a combination is better than either alone, which I did find support for. It contributes to educational technology through (3) the design of an effective ITS that supports collaborative and individual learning for fractions and educational data mining through (4) the advancement of models that can more accurately predict individual learning within a collaborative setting than the existing individual models. Finally, it contributes to computer supported collaborative learning and human-computer interaction through (5) a framework, which provides a lens for designing and analyzing combined collaborative and individual learning spaces, and (6) an orchestration prototype that supports fluid transitions between social planes in a way that can be a useful to both researchers and teachers in the classroom.

Over a period of nine months in 1999, a longitudinal teaching intervention was undertaken with Grade 3 learners in the Fort Beaufort district, Eastern Cape. Working in the interpretive paradigm, the intervention focussed on: - the development of the common fraction concept, - the relevance of the hierarchy of Murray and Olivier’s Four Levels of Development in common fractions and - whether learners’ informal knowledge could be utilised in developing this concept. Using the Problem-centred approach to teaching mathematics, problems set in reallife contexts were used as vehicles for learning. Learners were required to discuss, reflect and make sense of the mathematics they were doing. Participant observation, completed worksheets and unstructured interviews with learners, formed the primary method of data collection. Learners’ work was analysed and classified according to the method used and manner in which the solution was notated. Results showed that learners were able to achieve a significant degree of success in developing a stable common fraction concept. Learners were afforded opportunities to construct their own ideas and to develop a deeper understanding of the concept. Many methods used were based on their informal knowledge of sharing. Learners made sense of realistic problems using drawings, and invented their own procedures. Apart from Level One, Phase Three, all Murray and Olivier’s Levels of Development could be identified during the research. This study will provide educators with valuable information on how learners solve mathematical problems involving fractions and how informal knowledge can be used as a foundation on which to build.